How to use Google API in flutter?

I can't add comments yet, so I'll just post it as an answer.

I kept trying to make a GoogleHttpClient as per the top answer, but on the import, it says "The library 'package:http/http.dart' doesn't export a member with the shown name 'IOClient'."

I found the answer here https://pub.dartlang.org/packages/http#-changelog-tab-, which says you should import IOClient separately as such: import 'package:http/io_client.dart';

I thought this might help out others who are new to flutter and its implementation of Google APIs.

This worked for me:

Logging in using package google_sign_in and then get auth headers from it:

import 'package:google_sign_in/google_sign_in.dart'
    show GoogleSignIn, GoogleSignInAccount;

import 'package:googleapis/people/v1.dart'
    show ListConnectionsResponse, PeopleApi;

useGoogleApi() async {
  final _googleSignIn = new GoogleSignIn(
    scopes: [
      'email',
      'https://www.googleapis.com/auth/contacts.readonly',
    ],
  );

  await _googleSignIn.signIn();

  final authHeaders = _googleSignIn.currentUser.authHeaders;

  // custom IOClient from below
  final httpClient = GoogleHttpClient(authHeaders); 

  data = await PeopleApi(httpClient).people.connections.list(
      'people/me',
      personFields: 'names,addresses',
      pageToken: nextPageToken,
      pageSize: 100,
  );
}

This is a custom IOClient implementation that automatically adds the auth headers to each request. The googleapis call support passing a custom HTTP client to be used instead of the default (see above)

import 'package:http/io_client.dart';
import 'package:http/http.dart';

class GoogleHttpClient extends IOClient {
  Map<String, String> _headers;

  GoogleHttpClient(this._headers) : super();

  @override
  Future<StreamedResponse> send(BaseRequest request) =>
      super.send(request..headers.addAll(_headers));

  @override
  Future<Response> head(Object url, {Map<String, String> headers}) =>
      super.head(url, headers: headers..addAll(_headers));

}